Geometrical interpretation of the functional measure for supersymmetric gauge theories and of the gauge invariant effective action
type: Item
instance of: scholarly article
title: Geometrical interpretation of the functional measure for supersymmetric gauge theories and of the gauge invariant effective action
zbMATH Open document ID: 0733.58048
DOI: 10.1016/0003-4916(91)90238-4
author: P. Ellicott
author: Gabor Kunstatter
author: David J. Toms
published in: Annals of Physics
publication date: 1991-01-01T00:00:00Z
review text: The standard quantization method for field theories involves functional path integration over fields. The formalism makes use of superspace, in which each point is a field over ordinary space. Since the fields themselves may commute or anti-commute, the resulting space is described by coordinates some of which commute and others anti-commute. Such a space is referred to as ``supersymmetric.'' Furthermore, the fields in question, Yang-Mills, are subject to transformations (gauge) which must leave the underlying physics unchanged and thus must leave invariant physically significant quantities. As a result, the functional integral must be done in an invariant way. This paper is concerned with describing in a geometrical way techniques for dealing with this problem. This involves first defining a metric on superspace leading to a gauge invariant measure. Next the gauge invariance of the Lagrangian itself must be assured, in particular when treated perturbatively. An invariant approach to this is then provided by the introduction of an invariant connection, leading to expansions involving covariant derivatives. This paper provides a brief overview of many aspects of these problems, together with some applications and bibliography.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 81S40
zbMATH DE Number: 4213081
zbMATH Keywords: supersymmetry
zbMATH Keywords: Yang-Mills
zbMATH Keywords: functional integration
zbMATH Keywords: superspace
reviewed by: Carl H. Brans
MaRDI profile type: Publication
full work available at URL: 0003-4916(91)90238-4
OpenAlex ID: W2017476503
cites work: Conservation of Isotopic Spin and Isotopic Gauge Invariance
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: Q3762246
cites work: Riemannian geometry in spaces with Grassmann coordinates
cites work: A global theory of supermanifolds
cites work: Q3344780
cites work: Quasigroup construction and first class constraints
cites work: Grassmannian Kaluza-Klein theory
cites work: On a Theory of Particles with Half-Integral Spin
Recommended article: On integrable structure and geometric transition in supersymmetric gauge theories
Recommended article: Geometrical origin of supersymmetric gauge theories
Recommended article: On gauge invariance of Wilsonian effective actions in (supersymmetric) gauge theories
Recommended article: The geometry of gauged (super)conformal mechanics
Recommended article: Supergeometry, super Riemann surfaces and the superconformal action functional
Recommended article: A ``Gaussian'' approach to computing supersymmetric effective actions
Recommended article: Q3777038
Recommended article: GEOMETRIC APPROACH TO SUPERSYMMETRY
Recommended article: Q3200268
Recommended article: Generalized action principle and extrinsic geometry for 1 superparticles
description: scientific article; zbMATH DE number 4213081